Easy part - mono vs fluoro tippet shouldn't make any difference in casting. I use both and don't notice any difference.

Hard part - line coils? Could you explain a bit more?

Is your line twisting up and tangling? or

Is the line curled on the water after the cast? not fully unrolling and landing straight?

Take a look at this Discover Tenkara article and watch the video that shows the "fly first" cast.
http://eat-sleep-fish.co.uk/content/2013/01/discover-tenkara

and read Jason Klass's Western vs Tenkara Casting - Different Strokes:

http://www.tenkaratalk.com/2012/03/w...erent-strokes/